Analysis of impulsive-smooth behavior for switched interconnections

This paper considers the impulsive-smooth behavior of a switched system interconnection described by the first-order kernel representation. The switched interconnection consists of past and future trajectories which are switched at a certain instant by an external switching mechanism. We derive necessary and sufficient conditions for the concatenability of the past and future behaviors both in the distributional and functional senses. If the past behavior is concatenable with the future one, every past trajectory can be continued by an appropriate future trajectory without causing any impulses.